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1、ComputationalFinanceandRiskManagementFinancialDataModelingandAnalysisinRGuyYollinAppliedMathematicsUniversityofWashingtonGuyYollin(Copyright?2013)FinancialDataModelingandAnalysisinRRegression1/67Outline1Spuriousregressionexample2Commontrendsandcointegration3Cointegrationexamples4
2、Testingforcointegration5ErrorcorrectionmodelsandtheJohansenmethod6TradingmodelsGuyYollin(Copyright?2013)FinancialDataModelingandAnalysisinRRegression2/67CointegrationreferencesPfa?,AnalysisofIntegratedandCointegratedTimeSerieswithR,2008Zivot,ModelingFinancialTimeSerieswithS-PLUS,
3、2005SDAFEchapter15GuyYollin(Copyright?2013)FinancialDataModelingandAnalysisinRRegression3/67Outline1Spuriousregressionexample2Commontrendsandcointegration3Cointegrationexamples4Testingforcointegration5ErrorcorrectionmodelsandtheJohansenmethod6TradingmodelsGuyYollin(Copyright?2013
4、)FinancialDataModelingandAnalysisinRRegression4/67SpuriousregressionRegressinganon-stationarytimeseriesonanothernon-stationarytimeseriesistypically?ameaninglessmodelcalledaspuriousregressionThespuriousregressionphenomenonisasfollows:coe?cientestimatesconvergetoanon-normalrandomva
5、riablenotnecessarilycenteredonzerocoe?cientt-stats:tβ→±∞asthesamplesizeT→∞D(zhuǎn)uetofalseassumptionthaterrorsareindependentR2→1asthesamplesizeT→∞Ared?agforpossiblespuriousregressioniswhenR2>DW,theDurbin-Watsonstatistic??"Spuriousregressionsineconometrics",JournalofEconometrics2,111-12
6、0.?ExceptinthecaseofcointegratedtimeseriesGuyYollin(Copyright?2013)FinancialDataModelingandAnalysisinRRegression5/67SpuriousregressionexampleRCode:Plotrandomtimeseries>set.seed(123456)>e1<-rnorm(500)>e2<-rnorm(500)>tt<-1:500>y1<-0.8*tt+cumsum(e1)>y2<-0.6*tt+cumsum(e2)>plot(as.ts(
7、cbind(y1,y2)),plot.type="single",col=c(2,4),ylab="y1,y2")400300y1,y220010000100200300400500TimeGuyYollin(Copyright?2013)FinancialDataModelingandAnalysisinRRegression6/67SpuriousregressionexampleRCode:Regressionanddiagnostics>lm.mod<-lm(y1~y2)>summary(lm.mod)Call:lm(formula=y1~y2)
8、Residuals:Min1QMedian3QMax-30.6541-11.52
